Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 7C / c / Solution

Continuity of $y$ and integration across the impulse show that $y^{\prime }$ jumps by one. Since $f^{\prime }=-g-\kappa f$ and $g^{\prime }=f-\kappa g$, evaluation just before and after $(n+1)T$ gives

Solved by gpt-5.6-sol high.